The energy introduced by the vibration begins to accumulate, in the oscillatory play between the kinetic energy acquired by the mass, and the potential energy, generated after a certain delay by the elastic component, depending on the natural period of the oscillator. This oscillatory amplitude increases, until a state of equilibrium is reached between the energy being introduced by the vibration, and the energy being dissipated, as a result of the elastic hysteresis in the structural materials, and the possible friction opposed to the movement of the mass. Both of these effects, jointly, represent the damping of the oscillator. When this damping is low, on account of the nature of the element, the amplitude of the oscillations can only be limited by introducing separate damping devices.
In the elements of the plants described above, the structural materials and elements used (insulators, metal structures) frequently have low energy absorption characteristics. Introducing vibration dampers into these elements may be, however, difficult; the dampers, to operate, need to detect the motion of the oscillator relative to the ground, But, in general, they cannot be coupled to the region of maximum displacements of the elements (upper part of a column, middle part of a beam), and must therefore be inserted or connected, in the definite form of vibration isolators, between the element and its supports (base of a column, supporting ends of a beam). However, these vibration isolators introduce considerable elasticity which is sometimes a distinct advantage, but in most cases represents a serious difficulty, even an insuperable one, because of the changes which this flexibility may have on other functional characteristics of the element.
The design of the vibration isolators themselves has been minimized because of the location problem, and it has been found that the isolators are often self-defeating, because of the displacements at other parts of the element, which become strongly amplified, as a consequence of the isolators' elasticity.
These difficulties have resulted in the use of, which the elements and parts of the abovementioned plants, the already known principle of the dynamic vibration absorber, which is a secondary oscillator fixed on the element, in the zone of its maximal displacements, and which transforms part of the energy into dynamic reaction pulses, with a period somewhat different to that of the principal oscillator. If the ratios of the masses and of the periods are correct, the reaction pulses will be adequate to reduce the oscillatory energy within the principal oscillator, and the oscillations will be limited by this dynamic effect, with a final result similar to what could have been obtained from an efficient set of vibration isolators.
From this explanation itself, it is believed evident that the dynamic absorber can only be operative if the values of its mass and its elasticity, are definitely determined for the principal oscillator involved, and then, only for certain periodic vibrations. In other cases, the pulses of the auxiliary mass could prove, at certain moments at least, self-defeating, and can contribute forced vibrations to increase the vibrational energy rather than to limit it.
In theory, this danger is overcome by introducing into the secondary oscillator an adequate damping: this oscillator may be, in this case, considered as a device which pumps out of the principal oscillator, a part of the energy, to dissipate it within itself. An excessive value for this damping could still cause undue dynamic reactions, but the dynamic absorbing will be effective, for a range of values of the mass and the elasticity of the auxiliary oscillator. Optimum effects could be obtained with masses between 10 and 20% of the principal one; natural frequencies within .+-.20% of the frequency of the principal oscillator, and auxiliary damping, between 10 and 20% of the critical.
If one intends to use a system of such auxiliary mass dampers of a standard design, even these values could be considered as demanding a too close matching to the element, for adequate efficiency. However, problems can arise, if one considers that there is a certain interaction between these values, within these ranges, and the fact that the vibrations we are interested in are, by nature, irregular and transient.